Someone who's life, situation, or story always has to be worse than everyone else's. A literal dick made of shit would be the perfect example of a shitdick, as no matter how shitty your life is, no one wants to be a dick made of shit.
"Fuck. I got my dick caught in the shredder."
"Yeah? Well I'm a dick made of shit. How do you feel now?"
"Man, I have cancer."
"Man, I have two kinds of cancer!"
"Dude, don't be such a shitdick!"